Use Stokes' Theorem to calculate the integral ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$ where vec$(F)=(y-x)vec(i)+(z-y)vec(j)+(x-z)vec(k)$ and $C$ is the circle $x^2+y^2=2$ in the $xy-$plane, oriented counterclockwise when viewed from above. NOTE: Enter the exact answer, or round to three decimal places.

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=$